Numerical simulation of the advection-diffusion-reaction equation using finite difference and operator splitting methods: Application on the 1D transport problem of contaminant in saturated porous media

The combined advection-diffusion-reaction (ADR) equation, which describe the transport problem of a contaminant in porous medium, does not generally admit an analytical solution. In general, when solving ADR numerical methods (such as finite differences, elements, splitting), for most practical problems, equation is too difficult to solve analytically. difference method oldest and commonly used solution this kind equation. Although newer techniques, such those based on elements splitting are appropriate equilibrium-type remains time-dependent phenomena. can also be written by equation; hence, our objective choose efficient study 1D its evolution medium. work, we will simulate using two different methods: ones. result compared with order discuss stability convergence each them methods. end, show that technical more problems comparison despite fact latter widely researchers. validation efficiency method, implemented simulation, tested 1D-transport saturated